3 Discussion

The OT we proposed as the counterpart of GRB 971227 is present in one frame only; therefore alternative explanations have to be considered. The analysis of the dark image and of the flat field allows us to exclude an instrumental defect. Moreover, the photometric profile of the OT is not compatible with a cosmic ray.

Let us consider the possible presence of an asteroid on December 27.9 in the error box of 1SAX J1257.3+5924. Down to R = 20 there is, on average, one of such objects for $\sim$50 square degrees at the ecliptic latitude ($+59^{\circ}$) of the OT (Boattini 1998). Since the profile and the FWHM ($\sim 2''$) of the OT are as the nearby stars, the upper limit of its apparent motion should be 2''/720 s. This constrains its position farther than the orbit of Saturn. Taking into account the dimensions of the field, the probability that the OT is an asteroid moving with a speed less than 4'/day is <10^-7. The probability to find a small planet near one of its stationary points or a head-on meteorite in a field of radius $1\hbox{$.\mkern-4mu^\prime$}5$ is still lower.

Thus we can find no reason to reject the object detected at Calar Alto. If this object is real and is the optical counterpart to GRB 971227, the observations taken at Loiano and by Djorgovski et al. (1998) fix severe constraints on its light curve, which shows one of the steepest declines known until now ($\alpha\gt 1.8$). It can be noted that among the eight so far detected OTs likely related to GRBs, also GRB 980326, GRB 980519 and (in the first part of the light curve) GRB 970228 present rapid power law decays with $\alpha \gt 2$.

These short-lived afterglows and the steepness of their decline lead us to think of a less energetic and less extended phenomenon, which could characterize a particular class of GRBs. In some cases (GRB 970616, GRB 970815, and possibly GRB 970111) the non-detection of optical counterparts could also be explained with this kind of rapid optical decline.

Acknowledgements

We wish to thank the referee D. Lamb for his comments and suggestions, and A. Boattini for significant discussions. This work was partially supported by the University of Bologna (Funds for selected research topics), by Russian Fund of Fundamental Research, by Spanish CICYT grant ESP95-0389-C02-02 and by German Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMF/DLR).